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A109224
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Minimum number of moves to solve the second Panex puzzle of order n of exchanging the two side towers.
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1
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3, 13, 42, 128, 343, 881, 2189, 5359, 13023, 31537, 76245, 184191, 444807
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listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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Conjecture: for n >= 5, a(n) = ((7/2) * (7 - (4 * sqrt(2))) * (1 + sqrt(2))^n) - (8 * n) - 2 + ((7/2) * (7 + (4 * sqrt(2))) * (1 - sqrt(2))^n). Confirmed to n = 13, and known to be an upper bound for all larger n.
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REFERENCES
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Mark Manasse et al., The Panex puzzle, in Tribute to a Mathemagician, Peters, 2005, pp. 145-161.
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LINKS
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Table of n, a(n) for n=1..13.
N. Baxter, Panex Puzzle Resources.
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CROSSREFS
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Cf. A109175.
Sequence in context: A121162 A146018 A145946 * A106050 A074425 A041499
Adjacent sequences: A109221 A109222 A109223 * A109225 A109226 A109227
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KEYWORD
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hard,more,nonn
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AUTHOR
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William Rex Marshall, Aug 19 2005
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EXTENSIONS
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a(9) (found by David Bagley in 2008) and a(10)-a(13) (found by Derek Kisman in 2010) communicated by William Rex Marshall, May 27 2011
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STATUS
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approved
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